I'm working on converting an external garage into an office.  I've removed the original flag roof and replaced with a pitched roof.  I designed and built the roof trusses myself.  I then put underlay on the timbers and tiles until the job was complete.  The tiles overlap and are screwed to the woodwork.

The problem is that the pitch of the roof is such that when the rain is at an angle, water gets in at a few spots.

The question is what's the best way to resolve this?  I don't want to redo the roof, so I was thinking of using Marine plywood secured inside immediately under the tiles with felt on the plywood creating a run off to the bottom of the roof and to the outside.

Would this work? Is there a better solution? 

I other thing I was thinking of was using expanding foam instead between the tiles to seal up any gaps or places where water could get in.